Answer: 16r²s²=(4rs)²
Step-by-step explanation:
[tex]16r^2s^2=\\\\4^2r^2s^2=\\\\(4rs)^2[/tex]
The measure of two remote interior angles of a triangle are x - 10 and 4x + 4 The exterior angle of the triangle measures 3x + 54 Solve for the measure of the exterior angle .
The measure of the exterior angle of the triangle is 144 degrees.
How to solve angles of a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Therefore, the measure of the two remote interior angles of a triangle are x - 10 and 4x + 4. The exterior angle of the triangle measures 3x + 54 .
Let's solve for the exterior angle.
x - 10 + 4x + 4 = 3x + 54
5x - 6 = 3x + 54
5x - 3x = 54 + 6
2x = 60
x = 60 / 2
x = 30
Therefore,
exterior angle = 3x + 54 = 3(30) + 54 = 90 + 54 = 144 degrees
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She begins at sea level, which is an elevation of 0 feet.
She travels straight down for 41 seconds at a speed of 4.9 feet per second.
She then ascends for 49 seconds at a speed of 3.2 feet per second.
After this 90-second period, how much time, in seconds, will it take for the scientist to travel back to sea level at 3.6 feet per second?
The scientist will take 23 seconds to get back to the sea level.
Let us calculate the distance covered by the scientist at the given speeds and at the specified times.
She travels down for 41 seconds at speed of 4.9 feet per second.
Distance travelled = 41 × 4.9 = 200.9 feet
Elevation = -200.9 feet
She then goes up for 49 seconds at speed of 3.2 feet per second.
Distance travelled = 49 × 3.2 = 156.8 feet
Elevation = -222.9 + 156.8 = -44.1
So she is at a depth of 44.1 feet below the sea level.
Time taken = 44.1 / 3.6 = 12.25 seconds
Therefore it will take her about 12.25 seconds to go back to the sea level.
The average surface level of one or more of the Earth's coastal bodies of water is known as mean sea level (MSL), which can be used to calculate heights like elevation.
There are several terminologies that describe the ebb and flow of the relationship between sea level and dry land.
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A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 24 grams. The jeweler made a total of 16 bracelets and necklaces using 258 grams of gold. Determine the number of bracelets made and the number of necklaces made.
Answer:
Bracelets: 7 Necklaces: 9
Step-by-step explanation:
b+n=16
6n+24n=258
b=-n+16
6(-n+16)+24n=258
-6n+96+24n=258
18n=162
n=9
6n+24(9)=258
6n+216=258
6n=42
n=7
B stands for bracelets
N stands for necklaces
write a function that will standardize a multivariate normal sample for arbitrary n and d. that is, transform the sample so that the sample mean vector is zero and sample covariance is the identity matrix. to check your results, generate multivariate normal samples and print the sample mean vector and covariance matrix before and after standardization.
The function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
According to a multivariate normal distribution with mean vector m and variance-covariance matrix M, then this random vector, X , will have the joint density function as shown:
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
where, |M| denotes the determinant of the variance-covariance matrix M and M^(-1) is just the inverse of the variance-covariance matrix M.
Hence, the function that will standardize a multivariate normal sample is
Ф(X) = (1/2π)^(p/2).|M|^(-1/2).exp(-1/2(X-m)'M^(-1)(X-m))
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At 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.
If he continues at this rate, at what time will he reach `10000` steps?
To cover 10000 steps the time taken will be 115 minutes and he will cover at 9:55 AM.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.
The time will be calculated as,
2000 steps ⇒ 23 minutes
1 Step ⇒ 23 / 2000 minutes
10000 steps ⇒ ( 23 x 10000) / 2000 minutes
10000 steps ⇒ 115 minutes
The time of covering 10000 steps will be at 9:55.
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Pls help me I need to submit this
(5) All snow geese can eat for 11.5 days before the research and rescue center runs out of supplies.
What is snow geese?
Despite having a reputation for having white feathers, many snow geese are actually blue geese, which are darker, gray-brown birds. These birds were formerly believed to be two distinct species, however it has recently been discovered that they are actually just two color variants of the same bird. The variation in color is controlled by a single gene.
9 snow geese are housed in the research and rescue center.
Each geese consumed 16 ounces of seeds, therefore that's how much.
Therefore, the amount of seeds consumed by 9 snow geese is equal to (16*9) ounces.
144 ounces of seeds were consumed by 9 snow geese.
There are currently 1,656 ounces of seeds.
Thus, the number of days before the center runs out of food is equal to the sum of the ounces of seeds eaten by the nine snow geese divided by the total ounces of seeds.
Days till the food center runs out of supplies = 1656/144
11.5 days are required until the center runs out of food.
Hence, all snow geese can eat for 11.5 days before the research and rescue center runs out of supplies.
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a positive integer divisor of 12! is chosen at random. the probability that the di-visor chosen is a perfect square can be expressed asmn, wheremandnare relativelyprime positive integers. what ism n?
The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
What exactly is meant by probability?Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring.Given: Randomly, a positive integer divisor of 12! is selected.
Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11
Total divisors of 12! = 11 × 6 × 3 × 2 × 2
Each number in the prime factorization must have an even exponent in order to construct a perfect square divisor. In the prime factorization, the divisor cannot have any factors of 7 and 11 because there is only one of each in 12!. There are 6 × 3 × 2 perfect squares as a result.The probability that the divisor chosen is a perfect square is given as:
(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)
= 1/22
=m/n
Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
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c.) In a class of 28 sophomores and juniors, 16 are
juniors. What percent of the class are sophomores?
The percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.
According to the question,
We have the following information:
Total number in a class including sophomores and juniors = 28
Number of juniors in the class = 16
Now, we have the number of sophomores in this class:
Total number in the class- Number of juniors in the class
28-16
12
Now, we can easily find the percent of sophomores in the class by following the given steps:
Number of sophomores*100/Number of sophomores and juniors
1200/28
42.86%
Hence, the percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.
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Given the equation negative 28 equals y over 7, solve for y.
196
4
−4
−196
please help me.
The linear equation:
-28 = y/7
Can be solved by multiplying both sides by 7, to get y = -196
How to solve the equations?Here we want to solve the equation:
-28 = y/7
And we want to solve this for the variable y.
To do so, we need to isolate said variable in one side of the equation, now remember that we can multiply both sides of the equation by the same number.
Then we can multiply both sides by 7 so we get:
-28*7 = (y/7)*7
-196 = y
The correct option is the last one.
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line bd is tangent to a circle with diameter ab. explain why the measure of angle bca must equal the measure of angle abd.
The measures of the angles BCA and ABD are equal because they are both right angles.
The line segment BD is a tangent to the circle with diameter AB. We need to find out the reason why the measure of angle BCA must be equal to the measure of angle ABD. The diagram is attached below.
Since AB is the diameter of the circle, it makes an angle equal to 180 degrees at the center of the circle. So the measure of the angle BCA is half of the angle produced by the diameter.
∠BCA = (1/2)×180° = 90°
Since the line BD is tangent to the circle, it will be perpendicular to the diameter. Hence, the angle formed by the diameter and the tangent must be the right angle.
∠ABD = 90°
Hence, both the angles are equal to each other.
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A skydiver fell toward Earth at a steady speed for 10.0 seconds. He fell 593 meters in that
time. What was his speed?
Answer:
59.3 meters/second
Step-by-step explanation:
593 / 10 = 59.3
The ratio 20mins to 1 hour can be written in the form 1:n find the value of n.
Answer:
1:3
n=3
Step-by-step explanation:
1 hour = 60 minutes
20:60
20÷20=1
60÷20=3
1:3
As the diameter (d) of a circle increases in size, the circumference (C)
increases Likewise, as the diameter decreases in size, so does the circumference,
The constant of variation between Cand dist. Describe the kind of variation
between eireumference and diameter Write the equation.
A train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. How far is the train from the station?
Answer
23
45
65
89
If a train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. The distance of the train from the station is C. 65.
How to find the distance?Using Pythagoreans theorem formula to find the distance
d² = a² + b²
Where:
d = distance =?
a= east for 33 miles
b = 56 miles south
Let plug in the formula
d = √33² + 56²
d = √ 1089 + 3136
d = √4225
d = 65 miles
Therefore the correct option is C.
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an airplane ticket has a perimeter of 58 cm and an area of 198 square cm. What are the dimensions of the ticket
The dimensions of the ticket are width is 11 cm and length is 18 cm.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
An airplane ticket has a perimeter of 58 cm and an area of 198 square cm.
Let W is the width of the ticket and L is the length of the ticket
The area of a credentials= L × W
198 = L × W ...(i)
The perimeter of a ticket = 2(L+W)
58 = 2(L+W)
29 = L + W
L = 29 - W ...(ii)
Substitute the value of L = 99 - W in equation (i)
198 = (29 - W) × W
198 = 29W - W²
0 = W² - 29W + 198
[tex]0=\left(W^2-11W\right)+\left(-18W+198\right)[/tex]
[tex]0=W\left(W-11\right)-18\left(W-11\right)[/tex]
[tex]0=\left(W-11\right)\left(W-18\right)[/tex]
W = 18 or 11
Substitute the value of W = 11 in equation (ii)
L = 29 - 11
L = 18
Thus, the dimensions of the ticket are width is 11 cm and length is 18 cm.
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When using re-grouping to solve 21 x 43, what are the four products that would be calculated and then added?
800 + 40 + 6 + 3
80 + 40 + 60 + 3
800 + 40 + 60 + 3
800 + 3
Using re-grouping to solve 21 x 43, the four products that would be calculated and then added is: 800 + 40 + 60 + 3.
How to find the products?Given data:
21 x 43
Now let make use of re-group to find the for product
21 x 43
So,
20 +1 = 21
40 + 3 =43
Hence,
(20+1) × (40+3)
Expand
(20 × 40) + (1 × 40) + (20 ×3) + (1 ×3)
800 + 40 + 60 + 3
= 903
Check:
21 x 43 = 903
800 + 40 + 60 + 3 =903
Therefore the correct option is C.
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Write the equation of a line in point slope form that has a slope of 2 and passes through the point (-2,5)
Answer:
y=2x+9
Step-by-step explanation:
Fill in the equation
5=2(-2)+b
Solve for b
5 = -4+b
9 = b
Put the original equation
y=2x+9
Need help
The equation of the line L1 is y = 3x - 2
The equation of the line L2 is 3y - 9x + 5 = 0
Show that these two lines are parallel
Here is a correlation, does it also represent causation? Explain you answer.
The number of additional calories consumed and the amount of weight gained.
Yes, there is causation between the two given variables, as the weight is related at some point with the amount of calories consumed.
What does correlation and causation mean?
For two variables x and y, we say that there is causation when, if we modify one of the variables, the other changes in response.
Correlation just means that the variables are related in some way (maybe both have a causation relationship with the same other variable)
So causation implies correlation.
Correlation does not imply causation.
In this case, we have the example:
x = The number of additional calories consumed
y = amount of weight gained.
Clearly, we have causation between x and y as larger is the value of x, larger will be the value of x.-
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Three friends go grocery shopping together and buy apples. Logan buys 4
pays $7.00. Lin buys 6 lb and pays $10.50. Chita buys 2 lb
pounds (lb) and
and pays
$3.50.
Identify the graph and unit price that represent the cost of the apples.
The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.
What is the slope of a line?
The slope of a line is the tangent of the angle that the line makes with the positive direction of the x-axis. It signifies the rise in the y-variable for a unit change in the x-variable.
If the line passes through the points (x, y) and (x, y), then the slope of the line, m = (y - y)/(x - x).
(2, 3) representing the purchase by Logan,
(5, 7.5) representing the purchase by Lin,
(3, 4.5) representing the purchase by Chita.
The unit price can be calculated by the slope of the line;
m = (7.5 - 4.5)/(5 - 3) = 3/2 = 1.5.
Hence, The relationship between the data, the line and the unit price of apples of $1.50 per pound is best represented by option C Graph.
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a javalina rancher wants to enclose a rectangular area and then divide it into 5 pens with fencing parallel to one side of the rectangle. there are 580 feet of fencing available to complete the job. what is the largest possible total area of the 5 pens?
When there is 580 feet of fencing available to complete the job, the largest possible total area of the 5 pens is 7008.33 feet.
What is an area?The quantity area expresses the extent of a region on a plane or curved surface.
STEP 1: We know that,
A=x y
The perimeter equals 580feet.
The equation is,
580=6x+2y
Step 2: Solving y terns with x,
y=-3x+290
This information will assist us in obtaining our Area equation in terms of a single variable (just in terms of x).
Step 3: Using the x-y relationship discovered in Step 2, write your Area equation in terms of x only. You should obtain
A=x y
A=x(-3x+290)
A=-3x²+290x
Step 4: Derive the area equation, A' = -6x+290
Step 5: Set A' = 0
-6x+290=0
x=290/6
x=48.33
Step 6: Find y by substituting 48.33 in x in the perimeter equation then,
y=-3(48.33)+290
y=145.01
Step 7: A=x y
A=(48.33)(145.01)
A=7008.33 feet
The largest possible total area of the 5 pens is 7008.33 feet
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a pair of shoes is on sale, the original price is $150.99 and they are 30% whats a new price after the discount?
Answer:
Price after discount is $105.69Step-by-step explanation:
It is assumed 30% is the discount.
Original price is $150.99, discount is 30%, sale price is:
150.99 - 30% = 150.99 × (1 - 0.3) = 150.99 × 0.7 = 105.69 (rounded)Write 22 as a percentage of 58
Give your answer correct to the nearest whole number.
Answer:
38%
Step-by-step explanation:
22 ÷ 58 = 0.3793...
Ans × 100 = 37.93%
As a whole number = 38%
Omar is hiring a painting company to paint the interior of his house. The table represents prices the painting company quoted Omar.
Write a two-variable linear equation to represent the total cost, c, given the square feet, s, of the house.
A: c=2.25s+1347.85
B: c=2.25s+2847.85
C: c=2.25s+4047.85
D: c=2.25s+7654.60
The linear equation to represent the total cost c = 2.25s + 1,347.85.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
Using slope
slope= ( 5847. 75 - 4074 . 85)/( 2000- 1200)
slope= 1800 - 800
slope= 2.25
and, slope- intercept form
c - 4047.85 = 2.25 ( s- 1200)
c - 4047.85 = 2.25s - 2700
c = 2.25s - 2700 + 4047.85
c = 2.25s + 1,347.85
Hence, linear equation to represent the total cost c = 2.25s + 1,347.85.
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(b) Expand and simplify.
(2x - 5) (x - 3)
help me pls
[tex] = 2x(x - 3) - 5(x - 3) \\ = 2 {x}^{2} - 6x - 5x + 15 \\ = 2 {x}^{2} - 11x + 15 [/tex]
ATTACHED IS THE SOLUTION
the coded values for a measure of brightness in paper (light reflectivity), prepared by two different processes, are as shown in the accompanying table for samples of size 9 drawn randomly from each of the two processes. do the data present sufficient evidence to indicate a difference in locations of brightness measurements for the two processes? give the attained significance level.
The level can be attained by light reflections.
What are light reflections?The law of reflection states that objects can either be observed through the light they emit or, more frequently, through the light they reflect. The law of reflection, which states that the angle of incidence and reflection must be equal, is observed by reflected light.The transition known as reflection flips a shape in a mirror line, also known as a line of reflection, such that each point is at the same distance from the mirror line as its reflected point.n mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflectionlearn more about reflections here:
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It is 5:15 now. What time was it 9 hours and 15 minutes ago?
Answer:
8:00
Step-by-step explanation:
Calculate time
It is 5:15 now.
Subtract 15 minutes
5:00
Subtract 9 hours
subtract 5 hours
12:00
Then subtract 4 hours
8:00
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
The equation of the parabola
f(x) = [tex]7x^2[/tex]
The standard vertex form of a parabola is
y = [tex]a(x-h)^2[/tex] + k
The coordinates of the vertex of a parabola = (3, 5)
Where (h, k) is the coordinates
From the given function of the parabola f(x) = [tex]7x^2[/tex]
The value of a = 7
Substitute the values in the vertex form of a parabola
y = [tex]7(x-3)^2[/tex] + 5
Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5
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i count in equal steps my first number is -2 my fifth number is 26 whats my third number
The required third number will be 12 when numbers are in the A.P.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given data as
first number = - 2
fifth number = 26
Assume that the given numbers are in the A.P.
The formula to find the general term of an arithmetic sequence is,
Tₙ = a₁ + (n-1)d ...(i)
Substitute the value of n = 5 and a₁ = -2 in the above formula
T₅ = a₁ + (5-1)d
26 = -2 + 4d
4d = 28
d = 7
For finding the third term (number):
T₃ = -2 + (3-1)7
T₃ = -2 + (2)7
T₃ = -2 + 14
T₃ = 12
Therefore, the required third number will be 12 when numbers are in the A.P.
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Does the diagram contain enough information to prove that line segment JK is parallel to line segment ML? Explain your answer.
I think so ya is does you just need to tell your teacher if you don't understand